[seqfan] Rank of n in the Odd/Even sequence

Eric Angelini Eric.Angelini at kntv.be
Tue Feb 3 16:49:23 CET 2009

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Hello David,

> Such standards can only be enforced by a reasonably objective formal
editorial review process. In the absence of such a process, the OEIS
will continue to collect chaff.

... yes, I fully agree with you.

Is the hereunder idea 'chaff' ?
;-)
Best,
É.

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S = 1, 1, 6, 58, 5829, 58292915, ...

S = 1

Question (a) : is "1" odd or even?
Question (b) : what is the rank of "1" in the Odd numbers seq.? http://www.research.att.com/~njas/sequences/A005408
Answer: "1" is the first odd integer, it's rank is = 1
Action : write this rank as a new term of S :

S = 1, 1,

Question (a) : is "11" (concatenation of all preceding digits) odd or even?
Question (b) : what is the rank of "11" in the Odd numbers seq.?
Answer: "11" is the 6th integer, it's rank is = 6
Action : write this rank as a new term of S :

S = 1, 1, 6,

Question (a) : is "116" (concatenation of all preceding digits) odd or even?
Question (b) : what is the rank of "116" in the Even numbers seq.? http://www.research.att.com/~njas/sequences/A005843
Answer: "116" is the 58th integer, it's rank is = 58
Action : write this rank as a new term of S :

S = 1, 1, 6, 58,

Question (a) : is "11658" (concatenation of all preceding digits) odd or even?
Question (b) : what is the rank of "11658" in the Even numbers seq.?
Answer: "11658" is the 5829th integer, it's rank is = 5829
Action : write this rank as a new term of S :

S = 1, 1, 6, 58, 5829, ...

... etc.

I have computed this array yesterday (by hand):

S(1) =  1, 1,  6,   58,     5829,    58292915, ...
S(2) =  2, 1, 11, 1056, 10555528, ...
S(3) =  3, 2, 16, 1608, 16080804, ...
S(4) =  4, 2, 21, 2111, 21106056, ...
S(5) =  5, 3, 27, 2664, 26636332, ...
S(6) =  6, 3, 32, 3166, 31661583, ...
S(7) =  7, 4, 37, 3719, 37186860, ...
S(8) =  8, 4, 42, 4221, 42212111, ...
S(9) =  9, 5, 48, 4774, 47742387, ...
S(10) = 10, 5, 53, 5277, 52767639, ...

Could someone extend this array (to the right) -- or at least S(1)?

Best,
É.

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